A Bertrand curve is defined as a special curve which shares its principal normals with another special curve, called Bertrand mate or Bertrand partner curve.
is a Bertrand curve, where a, [xi] are constant numbers.
The spherical curve f is a circle if and only if the corresponding Bertrand curve is a circular helix.
s]) whose principal normal direction coincides with that of original curve, then [gamma] is said to be a Bertrand curve.
Let [gamma] be a Bertrand curve with a[kappa] + b[tau] = 1 and [bar.
Conversely, every Bertrand curve can be represented in this form.
at each pair of corresponding points coincide with the line joining corresponding points then [subset] is called a Bertrand curve and the curve [?
whenever it is well defined, then c is called a weakened Bertrand curve and denoted by W B curve.
Classical differential geometry of the curves may be surrounded by the topics which are general helices, involute-evolute curve couples, spherical curves and Bertrand curves
On spacelike constant slope surfaces and Bertrand curves
in Minkowski 3-space.
Ravani and Ku transported the notion of Bertrand curves to the ruled surfaces and called them Bertrand offsets .
A generalization of the Bertrand curves as general inclined curves in En.